Discover Vedic Mathematics

Description

This book shows how the Vedic system applies in a large number of areas of elementary mathematics, covering arithmetic, algebra, geometry, calculus etc. Each chapter concentrates on one Vedic Sutra or Sub-sutra and shows many applications. This gives a real feel for the Vedic Sutras each of which has its own unique character. It covers much of the content of Bharati Krsna's book above but in more detail and with more applications and explanations. It also contains Vedic solutions to GCSE and 'A' level examination questions, and an explanation of the Vedic Sutras themselves.

Details

Reviews

Discover Vedic Mathematics was tremendous - it is a system, and makes so many things perfectly comprehensible - Matthew Kirk, teacher

Just a quick note to say that your book, Discover Vedic Mathematics, is absolutely wonderful! Your examples and explanations are comprehensive in their scope; upon reading the text, working out the sample problems, and completing the corresponding exercises, I feel that I am well on my VM journey! - Dawn Dee Ahem, Maths teacher

Preface

This book consists of a series of examples, with explanations, illustrating the scope and versatility of the Vedic mathematical formulae, as applied in various areas of elementary mathematics. Solutions to 'O' and 'A' level examination questions by Vedic methods are also given at the end of the book.

The system of Vedic Mathematics was rediscovered from Vedic texts earlier this century by Sri Bharati Krsna Tirthaji (1884-1960). Bharati Krsna studied the ancient Indian texts between 1911 and 1918 and reconstructed a mathematical system based on sixteen Sutras (formulas) and some sub-sutras. He subsequently wrote sixteen volumes, one on each Sutra, but unfortunately these were all lost. Bharati Krsna intended to rewrite the books, but has left us only one introductory volume, written in 1957. This is the book "Vedic Mathematics" published in 1965 by Banaras Hindu University and by Motilal Banarsidass.

The Vedic system presents a new approach to mathematics, offering simple, direct, one-line, mental solutions to mathematical problems. The Sutras on which it is based are given in word form, which renders them applicable in a wide variety of situations. They are easy to remember, easy to understand and a delight to use.

The contrast between the Vedic system and conventional mathematics is striking. Modern methods have just one way of doing, say, division and this is so cumbrous and tedious that the students are now encouraged to use a calculating device. This sort of constraint is just one of the factors responsible for the low esteem in which mathematics is held by many people nowadays.

The Vedic system, on the other hand, does not have just one way of solving a particular problem, there are often many methods to choose from. This element of choice in the Vedic system, and even of innovation, together with the mental approach, brings a new dimension to the study and practice of mathematics. The variety and simplicity of the methods brings fun and amusement, the mental practice leads to a more agile, alert and intelligent mind, and innovation naturally follows.

It may seem strange to some people that mathematics could be based on sixteen word-formulae; but mathematics, more patently than other systems of thought, is constructed by internal laws, natural principles inherent in our consciousness and by whose action more complex edifices are constructed. From the very beginning of life there must be some structure in consciousness enabling the young child to organise its perceptions, learn and evolve. If these principles (see Appendix) could be formulated and used they would give us the easiest and most efficient system possible for all our mental enquiries. This system of Vedic Mathematics given to us by Sri Bharati Krsna Tirthaji points towards a new basis for mathematics, and a unifying principle by which we can simultaneously extend our understanding of the world and of our self.

In the chapters that follow each example shows a different application of the formula which is the subject of that chapter. A letter with a page number at the end of a section of a chapter indicates that an exercise on that section will be found at the end of the chapter.

This book was first published in 1984, one hundred years since the birth of Bharati Krsna. In this edition some new variations have been added as well as many comparisons with the conventional methods so that readers can clearly see the contrast between the two systems. An Appendix has been added that describes each of the sixteen Sutras as a principle or natural law. In this edition also is a proof of a class of equations coming under the Samuccaya Sutra by Thomas Dahl of Kristianstad University, Sweden (see Chapter 10).

Contents

PREFACE vILLUSTRATIVE EXAMPLES viii

1 All from Nine and the Last from Ten 1

SUBTRACTION 1MULTIPLICATION 2One number above and one below the Base 4Multiplying numbers near different bases 4Using other bases 5Multiplication of three or more numbers 7First corollary: squaring and cubing of numbers near a base 9Second corollary: squaring of number beginning or ending in 5 etc. 10Third corollary: multiplication of nines 12DIVISION 12THE VINCULUM 16Simple applications of the vinculum 18Exercises on Chapter 1: 20-

2 Vertically and Crosswise 25

MULTIPLICATION 25Number of zeros after the decimal point 28Multiplying from left to right 29Using the vinculum 30Algebraic products 31Using pairs of digits 31The position of the multiplier 31Multiplying a long number by a short number: The moving multiplier method 32Base five product 33STRAIGHT DIVISION 33Two or more figures on the flag 36ARGUMENTAL DIVISION 38Numerical application 39SQUARING 40SQUARE ROOTS 42Working two digits at a time 44Algebraic square roots 44FRACTIONS 45Algebraic Fractions 47LEFT TO RIGHT CALCULATIONS 48Pythagoras theorem 48Equation of a line 49Exercises on Chapter 2: 50-

SAMUCCAYA AS A COMMON FACTOR 104SAMUCCAYA AS THE PRODUCT OF THE INDEPENDENT TERMS 104SAMUCCAYA AS THE SUM OF THE DENOMINATORS OF TWO FRACTIONS HAVING THE SAME NUMERICAL NUMERATOR 105SAMUCCAYA AS A COMBINATION OR TOTAL 105Cubic equations 108Quartic equations 108THE ULTIMATE AND TWICE THE PENULTIMATE 109Exercises on Chapter 10: 109-

11 The First by the First and the Last by the Last 111

FACTORISING 112

12 By the Completion or Non-Completion 114Exercises on Chapter 12: 116-

13 By One More than the One Before 118

RECURRING DECIMALS 118Auxiliary fractions A.F. 121Denominators not ending in 1, 3, 7, 9: 124Groups of digits 126Remainder patterns 127Remainders by the last digit 128DIVISIBILITY 129Osculating from left to right 131Finding the remainder 132Writing a number divisible by a given number 132Divisor not ending in 9: 132The negative osculator Q 133P + Q = D 134Divisor not ending in 1, 3, 7, 9: 134Groups of digits 135Exercises on Chapter 13: 136-

Back Cover

Since the reconstruction of this ancient system interest in Vedic Mathematics has been growing rapidly. Its simplicity and coherence are found to be astonishing and we begin to wonder why we bother with our modern methods when such easy and enjoyable methods are available.

This book gives a comprehensive introduction to the sixteen formulae on which the system is based, showing their application in many areas of elementary maths so that a real feel for the formulae is acquired.

Using simple patterns based on natural mental faculties, problems normally requiring many steps of working are shown to be easily solved in one line, often forwards or backwards

Vedic Mathematics solutions of examination questions are also given, and in this edition comparisons with the conventional methods are shown, and also an account of the significance of the Vedic formulae (Sutras).